1. Field of the Invention
The present invention relates to a multi-hysteresis voltage controlled current source (VCCS) system.
2. Description of the Related Art
In recent years, active researches have been conducted on the “hybrid dynamical system” that contains the continuous variables and the discrete variables in the system. Although the existing computer systems are constituted as a discrete system based on the binary-logic variables, the presence of the hybrid dynamical systems equivalent to the Turing machines has been proved mathematically (see Non-Patent Document 1 below). Thus, there is a possibility that the computing systems different from the existing digital computers can be constituted using the hybrid dynamical system. Moreover, when the hybrid dynamical system presents very complex phenomena such as chaos, the dynamic and complex information processing methods are also conceivable by representing the attractors of the continuous variables with discrete values.
On the other hand, the chaos generating circuits using hysteresis elements have been proposed (see Non-Patent Documents 2-11 below). These circuits use the piecewise linear single-hysteresis elements as non-linear elements, and a variety of interesting chaotic attractors have been reported. Moreover, in order to make the chaotic attractors more diverse, the method has been proposed wherein the single-hysteresis elements are replaced by multi-hysteresis elements that can obtain multivalued outputs (see Non-Patent Documents 12-14 below). In this method, grid-scroll chaotic attractors or the like can be observed. The shapes of such complex chaotic attractors depend on the multi-hysteresis characteristics to be used.    Non-Patent Document 1: Michael S. Branicky, “Universal computation and other capabilities of hybrid and continuous dynamical systems”, Theoretical Computer Science, vol. 138, pp. 67-100, 1995    Non-Patent Document 2: R. W. Newcomb and S. Sathyan, “An RC op amp chaos generator”, IEEE Trans. on Circuits and Systems, Part I, Fundam. Theory Appl., vol. 30, no. 1, pp. 54-56, 1983    Non-Patent Document 3: R. W. Newcomb and N. El-Leithy, “A binary hysteresis chaos generator”, in Proc. of 1984 IEEE Int'l Symp. on Circuits and Systems, pp. 856-859, 1984    Non-Patent Document 4: Toshimichi Saito, “On a hysteresis chaos generator”, in Proc. of 1985 IEEE Int'l Symp. on Circuits and Systems, pp. 847-849, 1985    Non-Patent Document 5: Takashi Suzuki and Toshimichi Saito, “On fundamental bifurcations from a hysteresis hyperchaos generator”, IEEE Trans. on Circuits and Systems, Part I, Fundam. Theory Appl., vol. 41, no. 12, pp. 876-884, 1994    Non-Patent Document 6: Toshimichi Saito and Shinji Nakagawa, “Chaos from a hysteresis and switched circuit”, Phil. Trans. R. Soc. Lond. A, vol. 353, no. 1701, pp. 47-57, 1995    Non-Patent Document 7: Toshimichi Saito and Kunihiko Mitsubori, “Control of chaos from a piecewise linear hysteresis circuit”, IEEE Trans. on Circuits and Systems, Part I, Fundam. Theory Appl., vol. 42, no. 3, pp. 168-172, 1995    Non-Patent Document 8: J. E. Varrientos and E. Sanchez-Sinencio, “A 4-D chaotic oscillator based on a differential hysteresis comparator”, IEEE Trans. on Circuits and Systems, Part I, Fundam. Theory Appl., vol. 45, no. 1, pp. 3-10, 1998    Non-Patent Document 9: A. S. Elwakil and M. P. Kennedy, “Chaotic Oscillators derived from Saito's double-screw hysteresis oscillator”, IEICE Trans. Fundamentals, vol. E82-A, no. 9, pp. 1769-1775, 1999    Non-Patent Document 10: Masaki Kataoka and Toshimichi Saito, “A 2-port VCCS chaotic oscillator and quad screw attractor”, IEEE Trans. on Circuits and Systems, Part I, Fundam. Theory Appl., vol. 48, no. 2, pp. 221-225, 2001    Non-Patent Document 11: F. Bizzarri, D. Stellardo, and M. Storace, “Bifurcation analysis and its experimental validation for a hysteresis circuit oscillator”, IEEE Trans. on Circuits and Systems, Part I, Regular Papers, vol. 53, no. 7, pp. 517-521, 2006    Non-Patent Document 12: Fengling Han, Xinghuo Yu, Yuye Wang, Yong Feng, and Guanrong Chen, “n-scroll chaotic oscillators by second-order systems and double-hysteresis blocks”, Electronics Letters, vol. 39, no. 23, pp. 1636-1637, 2003    Non-Patent Document 13: Fengling Han, Xinghuo Yu, and Jiankun Hu, “A new way of generating grid-scroll chaos and its application to biometric authentication”, in Proc. of IEEE 2005 Industrial Electronics Society, 31st Annual Conference, pp. 61-66, 2005    Non-Patent Document 14: Fengling Han, Xinghuo Yu, Yong Feng, and Jiankun Hu, “On multiscroll chaotic attractors in hysteresis-based piecewise-linear systems”, IEEE Trans. on Circuits and Systems, Part II, Express Briefs, vol. 54, no. 11, pp. 1004-1008, 2007    Non-Patent Document 15: Takuya Hamada, Yoshihiko Horio, and Kazuyuki Aihara, “An IC implementation of a hysteresis two-port VCCS chaotic oscillator”, in Proc. of European Conf. on Circuits Theory and Design, pp. 926-929, 2007    Non-Patent Document 16: Takuya Hamada, Yoshihiko Horio, and Kazuyuki Aihara, “Experimental observations from an integrated hysteresis two-port VCCS chaotic oscillator”, in Proc. IEEE Int'l Work-shop on Nonlinear Dynamics of Electronic Systems, pp. 237-240, 2007    Non-Patent Document 17: Takuya Hamada, Yoshihiko Horio, and Kazuyuki Aihara, “A Fully-Differential Hysteresis Two-Port VCCS Chaotic Oscillator”, IEICE Technical Report, NLP2007-180, pp. 79-84, 2008